Boundary conditions in computational fluid dynamics: Difference between revisions

Revision as of 10:46, 7 December 2012

Revision as of 11:26, 7 December 2012

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[[File:Fig 1 Formation of grid in cfd.JPG|thumb|AddFig caption1 hereFormation of grid in cfd]]Almost every [[computational fluid dynamics]] problem is defined under the limits of initial and boundary conditions. For implementation of boundary conditions when we construct a staggered grid we add an extra node across the physical boundary in order to get,

*The nodes just outside the inlet of the system are used to assign the inlet conditions

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==Intake boundary conditions==

We are considering the case of an inlet perpendicular to the x-direction -[[File:Fig.2 u-velocity cell at intake boundary.JPG|left|thumb|Fig.2 u-velocity cell at intake boundary]]

[[File:Fig.4 pressure correction cell at intake boundary.JPG|thumb|Fig.4 pressure correction cell at intake boundary]]

[[File:Fig.3 v-velocity cell at intake boundary.JPG|center|thumb|Fig.3 v-velocity cell at intake boundary]]

[[File:Fig. 5 scalar cell at intake boundary.JPG|left|thumb|Fig. 5 scalar cell at intake boundary]]

*For the first u, v, φ-cell all links to neighboring nodes are active, so there is no need of any modifications to discretion equations.

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*Generally [[computational fluid dynamics]] codes estimate k and ε with approximate formulate based on turbulent intensity between 1 and 6% and length scale

==Symmetry boundary condition==

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Consider situation solid wall parallel to the x-direction:

[[File:Fig.6 u-velocity cell at a physical boundary.JPG|left|thumb|Fig.6 u-velocity cell at a physical boundary]]

[[File:Fig.8 v-cell at physical boundary j=NJ.JPG|thumb|Fig.8 v-cell at physical boundary j=NJ]]

[[File:Fig.7 v-cell at physical boundary j=3.JPG|center|thumb|Fig.7 v-cell at physical boundary j=3]]

[[File:Fig.9 scalar cell at a physical boundary.JPG|left|thumb|Fig.9 scalar cell at a physical boundary]]

'''Assumptions made and relations considered'''-

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*High Reynolds number

*No chemical reactions at the wall

==cyclic boundary condition==

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==Pressure boundary condition==

[[File:Fig.10 p’-cell at an intake boundary.JPG|left|thumb|Fig.10 p’-cell at an intake boundary]]

[[File:Fig. 11 p’-cell at an exit boundary.JPG|thumb|Fig. 11 p’-cell at an exit boundary]]

These conditions are used when we don’t know the exact details of flow distribution but boundary values of pressure are know

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*The pressure corrections are taken zero at the nodes.

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==exit boundary conditions==

Considering the case of an outlet perpendicular to the x-direction -

[[File:Fig.12 A control volume at an exit boundary.JPG|left|thumb|Fig.12 A control volume at an exit boundary]]

[[File:Fig. 14 pressure correction cell at an exit boundary.JPG|thumb|Fig. 14 pressure correction cell at an exit boundary]]

[[File:Fig. 13 v-control volume at an exit boundary.JPG|center|thumb|Fig. 13 v-control volume at an exit boundary]]

[[File:Fig.15 scalar cell at an exit boundary.JPG|left|thumb|Fig.15 scalar cell at an exit boundary]]

In fully developed flow no changes occurs in flow direction, gradient of all variables except pressure are zero in flow direction

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<math>U_{NI,J} = U_{NI-1,J}\frac{M_{in}}{M_{out}}\,</math>.

==References==

<references/>

*An introduction to computational fluid dynamics by Versteeg,PEARSON.